The tiebreaker rules come in when two people try to claim the same child. Since the mother cannot legally claim her for the EITC, due to having the ITIN, then there are not two people who could claim her for the EITC so the tiebreaker rules would not apply in this situation. However, if the mother claims the daughter as a dependent on her return, then the brother could not claim her for the EITC.
Also, if the mother claims the brother as a dependent on her return, the brother cannot claim the child as a dependent cannot claim another dependent.
If the family all lives together in the same house and the brother is not paying more than half of the cost to maintain the home, be sure that the brother does not claim head of household as that is one of the criteria to claiming head of household.
He can still claim the child as a dependent and still claim the EITC, but not Head of Household.
If the mother had a SSN instead of an ITIN, the tiebreaker rule would apply and the brother could not claim the child since the mothers AGI is higher.
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